相关论文: Weighted Divergent Beam Ray Transform: Reconstruct…

We advance a phase-space theory of partially coherent accelerating, non-diffracting beams employing the Wigner distribution function (WDF). We derive a general expression for the WDF of any accelerating, diffraction-free beam of arbitrary…

We explore the idea of restoring the full diffeomorphism (Diff) invariance in theories with only transverse diffeomorphisms (TDiff) by the introduction of additional fields. In particular, we consider in detail the case of a TDiff invariant…

This article extends the author's past work [Inv. Probl. Imaging, 10:2 (2016), 433--459] to attenuated X-ray transforms, where the attenuation is complex-valued and only depends on position. We give a positive and constructive answer to the…

We study the problem of inverting a restricted transverse ray transform to recover a symmetric $m$-tensor field in $\mathbb{R}^3$ using microlocal analysis techniques. More precisely, we prove that a symmetric $m$-tensor field can be…

In this paper we prove several new stability results for the reconstruction of binary images from two projections. We consider an original image that is uniquely determined by its projections and possible reconstructions from slightly…

We study radial symmetric point defects with degree $\frac {k}{2}$ in 2D disk or $\mathbb{R}^2$ in $Q$-tensor framework with singular bulk energy, which is defined by Bingham closure. First, we obtain the existence of solutions for the…

Vector beams, whose polarization varies across the transverse profile, are a central resource in structured-light optics and quantum photonics. Their characterization, however, becomes challenging when the field lies in a spectral region…

Decades of work on beam deformation on reflection, and especially on lateral shifts, have spread the idea that a reflected beam is larger than the incident beam. However, when the right conditions are met, a beam reflected by a multilayered…

We consider an inverse problem for a Westervelt type nonlinear wave equation with fractional damping. This equation arises in nonlinear acoustic imaging, and we show the forward problem is locally well-posed. We prove that the smooth…

In this paper, we consider the problem of recovering a compactly supported multivariate function from a collection of pointwise samples of its Fourier transform taken nonuniformly. We do this by using the concept of weighted Fourier frames.…

We prove the uniqueness and nondegeneracy of least-energy solutions of a fractional Dirichlet semilinear problem in sufficiently large balls and in more general symmetric domains. Our proofs rely on uniform estimates on growing domains, on…

In this work we investigate the unique identifiability and stable recovery of a spatially dependent variable-order in the subdiffusion model from the boundary flux measurement. We establish several new unique identifiability results from…

We develop an algorithm for reconstruction of elastic strain fields from their Longitudinal Ray Transform (LRT) in either two or three dimensions. In general, the LRT only determines the solenoidal part of a symmetric tensor field, but…

We study an inverse problem for the fractional wave equation with a potential by the measurement taking on arbitrary subsets of the exterior in the space-time domain. We are interested in the issues of uniqueness and stability estimate in…

The paper study recovery problem for discrete time signals with a finite number of missing values. The paper establishes recoverability of these missing values for signals with Z-transform vanishing with a certain rate at a single point.…

Gabor phase retrieval is the problem of reconstructing a signal from only the magnitudes of its Gabor transform. Previous findings suggest a possible link between unique solvability of the discrete problem (recovery from measurements on a…

Fractonic matter with dipole symmetry can be coupled to a two-index symmetric tensor gauge field. In this work, we show that this symmetric tensor field, along with other related generalized Maxwell theories, can be consistently coupled to…

In this work, we investigate an inverse problem of recovering multiple orders in a time-fractional diffusion model from the data observed at one single point on the boundary. We prove the unique recovery of the orders together with their…

In this work, we present and investigate the novel blind inverse problem of position-blind ptychography, i.e., ptychographic phase retrieval without any knowledge of scan positions, which then must be recovered jointly with the image. The…

The infinitesimal generator of a one-dimensional strictly $\alpha$-stable process can be represented as a weighted sum of (right and left) Riemann-Liouville fractional derivatives of order $\alpha$ and one obtains the fractional Laplacian…